Structure earthquake damage prediction method based on displacement autocorrelation sensitivity

Abstract

The invention discloses a structure earthquake damage prediction method based on displacement self-correlation sensitivity, relates to the technical field of earthquake damage response prediction, and aims to solve the problem of low earthquake damage prediction accuracy caused by data interference in the prior art. Complex de-noising processing is avoided, interference of multi-source noise can be effectively handled, and therefore the accuracy of earthquake damage prediction is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of earthquake damage response prediction, and particularly to a structural earthquake damage prediction method based on displacement autocorrelation sensitivity. Background Art

[0002] In recent decades, earthquakes have caused heavy casualties and property losses. As the main place for people's production and life, cities have gathered a large number of people and wealth. Once a large earthquake occurs, it will have a significant impact on cities. Therefore, the prediction of urban building earthquake damage is of great importance.

[0003] Currently, structural earthquake damage prediction methods usually rely on the accuracy of response data, especially the update process based on dynamic response data such as acceleration and displacement. Existing technologies generally invert the unknown parameters of the structure by comparing the error between the measured data and the model calculation results, and usually use filtering or denoising techniques to process noise. For example, some traditional methods will use denoising methods such as Gaussian filtering, moving average, Fourier transform, and wavelet transform to preprocess the data. However, these denoising processes not only reduce the prediction efficiency, but also still lead to the problem of low earthquake damage prediction accuracy when the noise is large. Summary of the Invention

[0004] The purpose of the present invention is to provide a structural earthquake damage prediction method based on displacement autocorrelation sensitivity for the problem of low earthquake damage prediction accuracy due to data interference in the prior art.

[0005] The technical solution adopted by the present invention to solve the above technical problems is as follows:

[0006] A structural earthquake damage prediction method based on displacement autocorrelation sensitivity includes the following steps:

[0007] Step 1: Construct a multi-degree-of-freedom shear model for simulating the earthquake response of a multi-story reinforced concrete frame structure;

[0008] Step 2: Obtain ground motion, apply the ground motion to the multi-degree-of-freedom shear model, and call finite element analysis software to obtain the structural displacement response. Then, add Gaussian white noise to the structural displacement response to obtain the measured displacement response;

[0009] Step 3: Obtain the autocorrelation function R of the measured displacement response e ;

[0010] Step 4: In the multi-degree-of-freedom shear model, initialize the stiffness change fraction α of each floor slab i to 0;

[0011] Step 5: Utilize the stiffness change fraction α of each floor slab iUpdate the multi-degree-of-freedom shear model. Then, based on the ground motion obtained in Step 2, after adding Gaussian white noise to the ground motion, input it into the updated multi-degree-of-freedom shear model, and call the finite element analysis software to obtain the structural displacement response and the structural velocity response. The structural displacement response is the predicted displacement response.

[0012] Step Six: Obtain the autocorrelation function \(R\) of the predicted displacement response a ;

[0013] Step Seven: Based on the structural displacement response and the structural velocity response obtained in Step Five, and using the Newmark-β method, obtain the displacement sensitivity.

[0014] Step Eight: Utilize the predicted displacement response and the displacement sensitivity to obtain the displacement autocorrelation sensitivity matrix.

[0015] Step Nine: Based on the autocorrelation function \(R\) of the measured displacement response e , the autocorrelation function \(R\) of the predicted displacement response a and the displacement autocorrelation sensitivity matrix, perform iteration using the damped least squares method and the singular value decomposition method to obtain the change amount \(\Delta\alpha\) of the stiffness change fraction.

[0016] Step Ten: Judge whether the convergence condition is satisfied according to \(\Delta\alpha\) obtained from two adjacent iterations. If not, let \(\alpha\) i =\(\alpha\) i +\(\Delta\alpha\), and repeat Steps Five to Nine until the convergence condition is satisfied, and output the final stiffness change fraction \(\alpha\) i , if satisfied, output the final stiffness change fraction \(\alpha\) i ;

[0017] Step Eleven: Obtain the ground motion to be evaluated, and combine it with the final stiffness change fraction \(\alpha\) i , use the motion equation of the linear damped structural dynamic system to obtain the displacement response of the structure, and obtain the earthquake damage assessment result according to the displacement response of the structure.

[0018] Furthermore, the specific steps of Step One are as follows:

[0019] Step 1-1: Obtain the geometric parameters, materials, loads, and mass distribution of the building structure.

[0020] Step 1-2: Obtain the length and width of each floor slab according to the geometric parameters of the building structure, and determine the unit area gravity value according to the materials and loads of the building structure.

[0021] Step 1-3: According to the mass distribution of the building structure, regard each floor slab as a concentrated mass node, connect the nodes with springs and dampers, and fix the bottom node of the building structure.

[0022] Step 14: Obtain the floor area based on the length and width of each floor slab, and multiply the floor area by the unit area gravity value to obtain the nodal mass m of the building structure;

[0023] Step 15: Obtain the fundamental period T1 of the building structure. Then, using the fundamental period T1 and the nodal mass m, and combining with the dynamic formula, obtain the inter-story stiffness k0;

[0024] Step 16: Based on the inter-story stiffness k0 and the nodal mass m, and using the dynamic formula, construct the global stiffness matrix and the mass matrix respectively;

[0025] Step 17: Based on the global stiffness matrix and the mass matrix, and combining with the Rayleigh damping model, construct the damping matrix.

[0026] Further, the dynamic formula is expressed as:

[0027]

[0028] Further, the damping ratio of the damping matrix is 5%;

[0029] Further, the structural displacement response is obtained through the following steps:

[0030] Apply the ground motion to the base nodes and use the Newmark-β method to obtain the structural displacement response of the structure under the earthquake action.

[0031] Further, the autocorrelation function R e of the measured displacement response and the autocorrelation function R a of the predicted displacement response are expressed as:

[0032]

[0033] where r ss [τ] is the autocorrelation of the signal z at the time delay τ, τ ∈ (0, N - 1), N is the length of the displacement time series, z k and z k+τ are the displacement values at the k-th moment and the (k + τ)-th moment respectively.

[0034] Further, the displacement autocorrelation sensitivity matrix is expressed as:

[0035]

[0036] where is the sensitivity of the displacement autocorrelation at different time delays τ, and are the displacement sensitivities at the k-th moment and the (k + τ)-th moment respectively.

[0037] Further, the specific steps of Step 9 are as follows:

[0038] Let R e -R a = b, Δα = x, and introduce Tikhonov regularization to obtain the objective function, which is expressed as:

[0039]

[0040] ||Ax - b|| 2 is the residual term, used to measure the matching degree between the solution x and the observed data b, λ is the regularization parameter, λ 2 ||x|| 2 is the regularization term;

[0041] The analytical solution of the Tikhonov regularized solution is expressed as:

[0042] x = (A T ·A + λ 2 I) -1 A T b

[0043] where A T is the transpose of matrix A, and I is the identity matrix with the same shape as A;

[0044] Perform singular value decomposition on matrix A, which is expressed as:

[0045] A = U∑V T

[0046] where U is the left singular matrix, ∑ is the singular value matrix, and V T is the transpose of the right singular matrix;

[0047] Substitute the singular value decomposition result into the analytical solution of the regularized solution, and let to obtain:

[0048]

[0049] where f is the Tikhonov filtering factor;

[0050] Use the L-curve method to determine the optimal regularization parameter λ in the x λ formula, and substitute λ into the analytical solution of the Tikhonov regularized solution to obtain the vector x of the change of the parameter to be updated, that is, Δα.

[0051] Further, the specific steps of using the L-curve method to determine the optimal regularization parameter λ in the x λ formula are as follows:

[0052] Step 1: Based on xλ , the second norm η of the solution and the second norm ρ of the residual are obtained;

[0053] Step 2: Take the logarithms of the second norm η of the solution and the second norm ρ of the residual respectively, to obtain and

[0054] Step 3: Use and to obtain the curvature κ, and the regularization parameter corresponding to the curvature κ is the optimal regularization parameter λ.

[0055] Furthermore, the convergence condition is:

[0056]

[0057] where is the change amount of the stiffness change fraction after the k-th iteration, is the change amount of the stiffness change fraction after the (k + 1)-th iteration.

[0058] The beneficial effects of the present invention are:

[0059] By considering the noise of ground motion and measured response, and using the displacement autocorrelation sensitivity analysis method, this application not only avoids complex denoising processing, but also can effectively cope with the interference of multi-source noise, thereby improving the accuracy of earthquake damage prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is a schematic diagram of the model update of this application;

[0061] Figure 2 is a schematic diagram of the influence of different levels of noise on the time series;

[0062] Figure 3 is the autocorrelation function graph of the time series under the influence of noise. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0063] It should be particularly noted that, without conflict, the various embodiments disclosed in this application can be combined with each other.

[0064] Detailed Embodiment 1: A structural earthquake damage prediction method based on displacement autocorrelation sensitivity described in this embodiment includes:

[0065] Step 1: Establish a simulated test model for simulating the measured response of the structure. The seismic response of a multi-story RC (reinforced concrete) frame structure is simulated using an MDOF (multi-degree-of-freedom) shear model. Among them, the establishment of the finite element model (MDOF (multi-degree-of-freedom) shear model) includes the following key steps:

[0066] First, obtain parameters such as the geometry, materials, loads, and mass distribution of the structure, and based on the geometric parameters of the structure, obtain the thickness, length, and width of each floor slab.

[0067] Secondly, take each floor slab as a lumped mass node, and connect the nodes with springs and dampers to represent stiffness and damping. The bottom node of the structure is fixed. The node mass m of the frame structure can be estimated by multiplying the unit area gravity value (11 - 14 kN / m 2 ) recommended in Article 5.1.8 of the Technical Specification for Concrete Structures of Tall Buildings by the floor area, where the lower limit of 11 kN / m is taken for low-rise or multi-story frames 2 , and the average value of 12.5 kN / m is taken for high-rise frames 2 . The fundamental period T1 of the structure can be calculated according to formula (21). The initial inter-story stiffness k0 is calculated from the fundamental period T1 and the mass m, and the stiffness of each floor is derived using dynamic formulas (such as ) to construct the global stiffness matrix and mass matrix; the Rayleigh damping model is used to form the damping matrix, and the damping ratio is taken as 5%. The inter-story stiffness of the test model can be set arbitrarily, and in this case, it is set to 1.2k0.

[0068] Step 2: Based on Step 1, use the real ground motion (without noise pollution) and call the OpenSees finite element analysis software to calculate the response of the structure. Apply the ground motion as an input to the base node (fixed), and use the Newmark-β method to calculate the displacement, velocity, and acceleration responses of the structure under the earthquake action, that is, solve equation (1). Add Gaussian white noise to the calculated displacement response to simulate the measured displacement response after being contaminated by noise (true response + noise = measured response).

[0069] Step 3: Calculate the autocorrelation function R of the measured displacement response according to formula (4) e ;

[0070] Step 4: Establish a finite element model for the predicted response. The model establishment method and parameter values are the same as in Step 1. Initialize the parameter α i (the stiffness change fraction of each layer of the structure), and the initial value is generally taken as 0.

[0071] Step 5: Add Gaussian white noise to the real ground motion, apply the ground motion as an input to the base node, and use the Newmark-β method to calculate the displacement, velocity, and acceleration responses of the structure under the earthquake action, that is, solve equation (1). Obtain the predicted response of the structure.

[0072] Step 6: Calculate the autocorrelation function R of the predicted displacement response according to formula (4) a ;

[0073] Step 7: Substitute the velocity and displacement vectors obtained by solving Equation (1) into Equation (3), and use the Newmark-β method to calculate the displacement sensitivity.

[0074] Step 8: Substitute the displacement obtained from Equation (1) and the displacement sensitivity obtained from Equation (3) into Equation (5) to calculate the displacement autocorrelation sensitivity matrix.

[0075] Step 9: Substitute the autocorrelation function \(R\) of the measured displacement e , the autocorrelation function \(R\) of the predicted displacement a and the displacement autocorrelation sensitivity matrix into Equation (6), and use the damped least squares method and the singular value decomposition method to iteratively solve for \(\Delta\alpha\). The specific process is as follows: Equation (6) can be simplified to the form of Equation (9); by introducing a regularization term, the objective function is modified to the form of Equation (10); by optimizing the objective function, the analytical solution of the Tikhonov regularization solution shown in Equation (11) can be obtained; according to Equation (12), perform singular value decomposition on the matrix \(A\) in Equation (11), substitute the singular value decomposition result into Equation (11), and Equation (13) can be obtained; use the L-curve method to determine the optimal regularization parameter \(\lambda\) in Equation (13), and calculate the two-norm of the solution and the two-norm of the residual according to Equations (14) and (15); substitute the results of regularization and singular value decomposition into Equations (14) and (15) to obtain Equations (16) and (17); take the logarithm of the norm of the solution and the norm of the residual according to Equations (18) and (19), and then substitute the calculation results into Equation (20) to calculate the curvature \(\kappa\) of the L-curve; the regularization parameter corresponding to the curvature \(\kappa\) is the optimal regularization parameter.

[0076] Step 10: Substitute the \(\Delta\alpha\) obtained from two adjacent iterative calculations into Equation (7) to determine whether the convergence condition is satisfied. When the convergence criterion in Equation (7) is satisfied or the predefined maximum number of iterations is reached, stop the calculation and output the final stiffness change fraction. Then use the relative percentage error shown in Equation (8) to measure the accuracy of the model update result. If neither the convergence criterion in Equation (7) is satisfied nor the predefined maximum number of iterations is reached, update the stiffness change fraction and repeat Steps 4 - 9;

[0077] Based on the stiffness change fraction, combined with the ground motion data to be measured, use the motion equation of the linear damped structural dynamic system to obtain the response (\(z\)) of the structure, and obtain the seismic damage assessment result according to the response of the structure (FEMA2012d Multi-hazad loss estimation methodology HAZUS-MH 2.1 engineering building module).

[0078] Displacement Sensitivity Calculation

[0079] The equation of motion of the linear damping structure dynamic system is expressed as:

[0080]

[0081] In the above formula, M is the mass matrix of the structure, C is the damping matrix, and K is the stiffness matrix. z is the displacement vector, is the velocity vector, is the acceleration vector. G is the mapping matrix from the force vector F to the corresponding degrees of freedom of the system.

[0082] The damping matrix adopts the most commonly used Rayleigh damping model:

[0083] C = α m M + β k K (2)

[0084] α m and β k are the mass proportional damping and the stiffness proportional damping respectively.

[0085] Taking the partial derivative of both sides of formula (1) with respect to α i yields:

[0086]

[0087] where α i is the stiffness change fraction of each layer of the structure, and are the acceleration sensitivity, velocity sensitivity, and displacement sensitivity respectively.

[0088] Both equations (1) and (3) are calculated using the Newmark direct integration method. The velocity response and displacement response of the system can be obtained through formula (1). Therefore, the right side of equation (3) can be regarded as a known force vector.

[0089] Calculation of displacement autocorrelation sensitivity

[0090] The autocorrelation function provides an important basis for analyzing time series characteristics by quantifying the similarity between a signal and its time-shifted version. In particular, Gaussian white noise has a significant attenuation of the autocorrelation value at non-zero delays due to its randomness, while the autocorrelation function of a periodic signal exhibits regular peaks at integer multiples of its fundamental frequency period. This characteristic difference makes autocorrelation analysis an effective means of distinguishing deterministic components from random noise.

[0091] As Figure 2 shown, as the signal-to-noise ratio (SNR) decreases, the increase in the proportion of noise energy causes obvious distortion of the signal waveform, and its time-domain characteristics tend to be blurred. It should be noted that after autocorrelation processing ( Figure 3) The function curves under different noise levels still maintain a highly similar peak distribution at the critical delay points, which verifies the strong robustness of this method against noise interference - by statistically averaging the time-domain signals, the random noise is effectively suppressed while the coherence characteristics of the periodic components are amplified.

[0092] The above analysis shows that the autocorrelation technique realizes the physical mechanism of signal-noise separation by deeply exploring the inherent time correlation of signals and combining the statistical decorrelation characteristics of noise. This adaptive processing method without prior knowledge makes it have important application value in the field of feature extraction and period recognition of noisy signals.

[0093] The measured displacement time series z of the structure k has an autocorrelation function as follows:

[0094]

[0095] In the above formula, r ss [τ] represents the autocorrelation of the signal z at the time delay τ, and N is the length of the displacement time series.

[0096] Taking the partial derivative of both sides of formula (4) with respect to the stiffness change fraction α i yields:

[0097]

[0098] Among them, is the sensitivity of the displacement autocorrelation at different time delays τ, and are the displacement sensitivities at time k and time k+τ respectively, z k and z k+τ are the displacement values at time k and time k+τ respectively.

[0099]

[0100] R e is the autocorrelation function of the measured displacement, R a is the autocorrelation function of the predicted displacement, is the sensitivity matrix of the predicted displacement autocorrelation, and Δα is the parameter vector to be updated.

[0101] The convergence criterion is:

[0102]

[0103] Among them, is the stiffness change fraction increment vector after the k-th iteration, is the stiffness change fraction increment vector after the (k + 1)-th iteration.

[0104] The relative percentage error is used to measure the accuracy of the model update result:

[0105]

[0106] where α pred is the predicted value of the stiffness change fraction vector, and α real is the true value of the stiffness change fraction vector.

[0107] Solving ill-conditioned equations

[0108] Tikhonov regularization

[0109] When solving ill-conditioned or ill-posed problems, Tikhonov regularization is a commonly used method. By adding a regularization term to the objective function, it suppresses the instability of the solution caused by ill-conditioned problems and improves the numerical stability and robustness of the solution.

[0110] Let R e -R a = b, Δα = x, then formula (6) can be expressed as:

[0111] Ax = b (9)

[0112] A is the sensitivity matrix, x is the vector of changes in the parameters to be updated, and b is the residual vector.

[0113] The objective function is:

[0114]

[0115] ||Ax - b|| 2 is the residual term, which measures the matching degree between the solution x and the observed data b. λ is the regularization parameter, and λ 2 ||x|| 2 is the regularization term, which is used to limit the size of the solution to prevent overfitting.

[0116] By optimizing the above objective function, the analytical solution of the Tikhonov regularized solution can be obtained:

[0117] x = (A T · A + λ 2 I) -1 A T b (11)

[0118] where A T is the transpose of matrix A, and I is the identity matrix with the same shape as A.

[0119] Singular value decomposition

[0120] Ill-conditioned linear equations are characterized by a very large condition number of the coefficient matrix A, meaning that small input errors can lead to large changes in the solution. This phenomenon is usually due to some singular values of the matrix being very small, even close to zero, making the inverse of the matrix unstable. Directly solving (such as using ordinary matrix inversion methods) will amplify the errors, while SVD can better control such errors. Therefore, the singular value decomposition method is used in the calculation of the pseudoinverse.

[0121] Perform singular value decomposition on matrix A:

[0122] A = UΣV T (12)

[0123] In the above formula, U is the left singular matrix, Σ is the singular value matrix, and V T is the transpose of the right singular matrix.

[0124] Substitute the singular value decomposition result into formula (11), and let We can get:

[0125]

[0126] In the above formula, f is the Tikhonov filtering factor.

[0127] Determine the optimal regularization parameter by the L-curve method

[0128] Calculate the two-norms of the solution and the residual

[0129] For different regularization parameters λ, the relationship between the residual norm and the solution norm forms an "L"-shaped curve, which is the so-called L-curve.

[0130] The two-norm of the solution and the two-norm of the residual are expressed as follows:

[0131] η = ||x λ ||2 (14)

[0132] ρ = ||Ax λ -b||2 (15)

[0133] Calculate the two-norm η of the solution and the two-norm ρ of the residual using the results of regularization and singular value decomposition:

[0134]

[0135] Determine the inflection point of the L-curve

[0136] The inflection point of the L-curve usually corresponds to the optimal λ. The λ values near the inflection point can not only make the solution have a good fit to the data but also maintain the stability of the solution and avoid excessive fluctuations. Because it balances the relationship between the smoothness of the solution and the fitting accuracy.

[0137] Take the logarithms of the 2-norm η of the solution and the 2-norm ρ of the residual respectively:

[0138]

[0139] The L-curve is a set of points in a double-logarithmic coordinate system. The inflection point is the point on the L-curve with the maximum curvature, and the curvature κ can be calculated by the following formula: The inflection point is the point on the L-curve with the maximum curvature, and the curvature κ can be calculated by the following formula:

[0140]

[0141] Numerical case analysis

[0142] To verify the effectiveness of the model updating method based on displacement autocorrelation sensitivity, a numerical simulation of the dynamic response of a two-dimensional three-degree-of-freedom frame structure under seismic loads was carried out. The length × width × height of the structure is 66×14.7×11.7m, with a total of 3 floors, and the height of each floor is 3.9m. It is assumed that each floor of the structure has the same mass and stiffness. The structure is designed according to Chinese codes. The seismic fortification intensity is 8 degrees, the design basic seismic acceleration is 0.2g, and the site category is II.

[0143] The MDOF shear model is used to simulate the seismic response of the multi-story RC frame structure. This model simplifies each floor into a mass point. The mass points between different floors are connected together by shear springs. The floor mass is calculated according to the gravity per unit area and the area of the building plan polygon. For the frame structure, the gravity per unit area is taken as 11 - 14kN / m according to the provisions of the Chinese code "Technical Specification for Concrete Structures of Tall Buildings". 2 The linear elastic stiffness of the story shear spring is calculated according to the floor mass and the fundamental period of the building. Among them, the fundamental period of the building is estimated according to formula (21), where T0 is the fundamental period, H is the total height of the structure, and B is the width of the structure. The inter-story sway stiffness of the frame structure is defined as the parameter to be updated.

[0144]

[0145] To simulate the influence of actual monitoring data at different noise levels, Gaussian white noise with different signal-to-noise ratios (30dB, 25dB, and 20dB) is superimposed on the ground motion and the simulated measured response respectively. By adjusting the random seed under the same signal-to-noise ratio condition, 10 groups of independent Gaussian white noises are generated to achieve the diversity of noise samples. Subsequently, the maximum and minimum values of the calculation results are removed, and the average value of the remaining 8 groups of calculation results is taken. This can reduce the accidental influence of random noise on the calculation results, thereby improving the robustness and reliability of the results.

[0146] As can be seen from Table 1, for the traditional model updating method based on displacement sensitivity, under noise-free conditions, the parameter normalization error of the calculation result is 0.000802; under the influence of Gaussian white noise at 30 dB, 25 dB, and 20 dB, the parameter normalization errors of the calculation results are 14%, 31%, and 46% respectively.

[0147] Table 1 Comparison of model updating results of a three-layer structure based on displacement sensitivity under different noise levels

[0148]

[0149]

[0150] As can be seen from Table 2, for the model updating method based on displacement autocorrelation sensitivity, the parameter normalization error under noise-free conditions is 0.003162; when Gaussian white noise with signal-to-noise ratios of 30 dB, 25 dB, and 20 dB is superimposed, its parameter normalization errors are 1%, 3%, and 5% respectively. Compared with the traditional model updating method based on displacement sensitivity, the model updating accuracy of this application under the above three noise conditions is improved by 93%, 90%, and 89% respectively.

[0151] It can be seen that, compared with the traditional method, the proposed displacement autocorrelation sensitivity method has achieved significant error reduction under different noise levels, demonstrating the significant advantages of this application in processing noisy monitoring data.

[0152] Table 2 Comparison of model updating results of a three-layer structure based on displacement autocorrelation sensitivity under different noise levels

[0153]

[0154]

[0155] This application can be widely applied to the health monitoring and evaluation of engineering structures, especially suitable for fields such as the structural safety assessment of buildings after earthquakes, the seismic performance analysis of urban area building groups, and the dynamic response monitoring and updating of building groups. It can significantly improve the finite element model updating accuracy under complex environmental conditions, reduce the sensitivity to noise, and does not require redundant denoising processing of the actual collected data.

[0156] It should be noted that the specific implementation manners are only explanations and illustrations of the technical solutions of the present invention, and the scope of the right protection cannot be limited thereby. Any changes that are only partial based on the claims and the description of the present invention should still fall within the protection scope of the present invention.

Claims

1. A structural earthquake damage prediction method based on displacement autocorrelation sensitivity, characterized in that The following steps are involved: Step 1: Construct a multi-degree-of-freedom shear model for simulating the seismic response of multi-story reinforced concrete frame structures; Step 2: Obtain earthquake motion, apply earthquake motion to multi-degree-of-freedom shear model, and call finite element analysis software to obtain structural displacement response, then add Gaussian white noise to the structural displacement response to obtain measured displacement response; Step 3: Obtain the autocorrelation function R of the measured displacement response e ; Step 4: In the multi-DOF shear model, change the stiffness fraction α of each floor slab i Initialized to 0; Step 5: Use the stiffness change fraction α of each floor i The multi-degree-of-freedom shear model is updated. Then, based on the earthquake motion obtained in step 2, Gaussian white noise is added to the earthquake motion, and the updated multi-degree-of-freedom shear model is input. The finite element analysis software is called to obtain the structural displacement response and structural velocity response, the structural displacement response, that is, the predicted displacement response; Step 6: Obtain the autocorrelation function R of the predicted displacement response a ; Step 7: Based on the structural displacement response and structural velocity response obtained in step 5, the displacement sensitivity is obtained by using the Newmark-β method; Step 8: Using the predicted displacement response and displacement sensitivity, obtain the displacement autocorrelation sensitivity matrix; Step 9: Autocorrelation function R based on measured displacement response e , the autocorrelation function R of the predicted displacement response a and displacement autocorrelation sensitivity matrix, and the damped least square method and singular value decomposition method are used to iterate and obtain the change of stiffness change fraction Δα; Step 10: Determine whether the convergence condition is met based on the Δα obtained from two adjacent iterations. If not, set α i =α i +Δα, and repeat steps 5 to 9 until the convergence condition is met, and output the final stiffness change fraction α i , if satisfied, then output the final stiffness change fraction α i ; Step 11: Obtain the ground motion to be evaluated and combine it with the final stiffness change fraction α i , using the motion equation of the linear damping structural dynamic system, the displacement response of the structure is obtained, and the earthquake damage assessment result is obtained based on the displacement response of the structure.

2. A structural earthquake damage prediction method based on displacement autocorrelation sensitivity according to claim 1, characterized in that The specific steps of step one are: Step 1: Obtain geometric parameters, materials, loads and mass distribution of the building structure; Step 1 and 2: Obtain the length and width of each floor slab according to the geometric parameters of the building structure, and determine the unit area gravity value according to the material and load of the building structure; Step 13: According to the mass distribution of the building structure, each floor slab is taken as a concentrated mass node, the nodes are connected by springs and dampers, and the bottom nodes of the building structure are consolidated; Step 14: According to the length and width of each floor slab, the floor area is obtained, and the floor area is multiplied by the unit area gravity value to obtain the node mass m of the building structure; Step 15: Obtain the basic period T1 of the building structure, and then use the basic period T1 and the node mass m, combined with the dynamic formula, to obtain the interlayer stiffness k0; Step 16: Based on the interlayer stiffness k0 and the node mass m, and using the dynamics formula, construct the overall stiffness matrix and mass matrix respectively; Step 17: Based on the overall stiffness matrix and mass matrix, and combined with the Rayleigh damping model, construct the damping matrix.

3. A structural earthquake damage prediction method based on displacement autocorrelation sensitivity according to claim 2, characterized in that The kinetic formula is expressed as:

4. A structural earthquake damage prediction method based on displacement autocorrelation sensitivity according to claim 2, characterized in that The damping ratio of the damping matrix is ​​5%.

5. The structural earthquake damage prediction method based on displacement autocorrelation sensitivity according to claim 1 is characterized in that The structural displacement response is obtained by the following steps: The earthquake motion is applied to the base nodes, and the Newmark-β method is used to obtain the structural displacement response of the structure under earthquake action.

6. The structural earthquake damage prediction method based on displacement autocorrelation sensitivity according to claim 1 is characterized in that The autocorrelation function R of the measured displacement response e and the autocorrelation function R of the predicted displacement response a It is expressed as: Among them, r ss [τ] is the autocorrelation of signal z at time lag τ, τ∈(0, N-1), N is the length of the displacement time series, z k and z k+τ are the displacement values ​​at time k and time k+τ respectively.

7. A structural earthquake damage prediction method based on displacement autocorrelation sensitivity according to claim 6, characterized in that The displacement autocorrelation sensitivity matrix is ​​expressed as: in, is the sensitivity of displacement autocorrelation at different time lags τ, and are the displacement sensitivities at time k and time k+τ respectively.

8. The structural earthquake damage prediction method based on displacement autocorrelation sensitivity according to claim 1 is characterized in that The specific steps of step nine are: make And introduce Tikhonov regularization to get the objective function, which is expressed as: ||Ax-b|| 2 is the residual term, which is used to measure the matching degree between the solution x and the observed data b, λ is the regularization parameter, 2 ||x|| 2 is the regularization term; The analytical solution of Tikhonov regularization solution is expressed as: x=(A T ·A+λ 2 I) -1 A T b Among them, A T is the transpose of matrix A, and I is the identity matrix of the same shape as A; Perform singular value decomposition on matrix A, expressed as: A=U∑V T Among them, U is the left singular matrix, Σ is the singular value matrix, V T is the transpose of the right singular matrix; Substitute the singular value decomposition result into the analytical solution of the regularization solution and let We can get: Where, f is the Tikhonov filter factor; Use L-curve method to determine x λ The optimal regularization parameter λ in the formula is substituted into the analytical solution of Tikhonov regularization solution to obtain the vector x of parameter changes to be updated, that is, Δα.

9. A method for predicting structural earthquake damage based on displacement autocorrelation sensitivity according to claim 8, characterized in that The L-curve method is used to determine x λ The specific steps for the optimal regularization parameter λ in the formula are: Step 1: Based on x λ , we get the second norm η of the solution and the second norm ρ of the residual; Step 2: Take the logarithm of the second norm of the solution η and the second norm of the residual ρ, respectively, and get and Step 3: Exploitation and The curvature κ is obtained, and the regularization parameter corresponding to the curvature κ is the optimal regularization parameter λ.

10. The structural earthquake damage prediction method based on displacement autocorrelation sensitivity according to claim 1 is characterized in that The convergence condition is: in, is the change in stiffness change fraction after the kth iteration, is the change in stiffness change fraction after the k+1th iteration.

Images